Here is an interesting quote that comes to my mind again and again:
You teach best what you most need to learn. (Richard Bach)
This coming winter I will be giving a course in function theory in several complex variables. As last year, I may use the blog to post some lecture notes for lectures that I will present in a somewhat different way than how it is done in the books I have. I don’t know yet the course number. The course will be between two to four hours a week. Probably it will be four.
Here is a very interesting introduction to the subject, by R. Michael Range, that gives a flavor of in what ways this subject is much more than a straightforward marriage of function theory in one complex variables and multi-variable calculus.
My incentives for offering this course are
- First of all, my need to use complex analysis in several variables has been steadily growing since the last year of my PhD studies, and I want to fasten all the knowledge I accumulated, get it organize in my head, and dive deeper.
- I am thinking of this course as part of the training that I owe my students and postdocs. These days working with me means, with high probability, doing something related to function theory in several complex variables.
- This is a beautiful, beautiful subject, which is very important to other fields such as algebraic geometry and some fancy physics (but now that we marked off “importance” we can safely forget about it — at least for now — and concentrate on “beautiful”), and should be given in our department from time to time, ve im lo achshav, eimatai?
This course will not be designed to ultimately reach my current research interests, because there are so many basic and classical material that I want to cover which come before my current interests, and are by far more important (and probably more interesting, to most students) than what I happen to be doing right now.